NEW YORK — It made little sense, but few of the 76ers’ games have this season.

How could a team with a season-high 26 turnovers keep the score close enough to stage a fourth-quarter comeback? While on the road, and after trailing by as many as 19 points, no less.

Somehow, the Sixers were in position to steal a game Monday night at Barclays Center. It didn’t work out that way, and the Brooklyn Nets surged at the right time to send away the Sixers, 108-102, with their 13th loss in 16 games.

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Their last turnover was the most bitter to swallow. With the Sixers trailing Brooklyn by four with 12 seconds to go, Michael Carter-Williams’ bounce pass to Evan Turner in the backcourt was mishandled and subsequently stolen by Shaun Livingston. It wiped out the work the Sixers had done earlier in the fourth to chisel away at the Nets’ one-time, 19-point lead and get it to two on two occasions.

“I can’t. I wish I could,” he said. “It continues to haunt us. We have to get more responsible with the ball. I have to do a better job. It bites us continually.”

The Sixers picked up 21 points from Carter-Williams, who was tied with Spencer Hawes with a team-worst six turnovers, as well. But in this game, who didn’t have a handful of turnovers for the Sixers?

The return of Carter-Williams was welcome by the Sixers (15-34), though it was somewhat shrouded in mystery. The rookie point guard pointed to a sore right shoulder as the cause for sitting out Saturday’s lopsided loss in Detroit. Then he wasn’t with the team as recently as Monday morning, missing the team’s shootaround in Brooklyn.

His time away from the team was to tend to personal reasons. Carter-Williams would not elaborate.

Sixers coach Brett Brown said the schedule — which included an off day Sunday — afforded Carter-Williams an opportunity to head to Massachusetts and handle his family issue.

In the locker room before the game, Carter-Williams said he was uncertain when he hurt his shoulder, but said he know how he hurt it: by trying to run through a screen. He said he had received treatment on the injured shoulder and declared himself eligible. Brown echoed that.

“It’s 100 percent enough,” Brown said.

Carter-Williams gave the Sixers a chance in a game in which they seemed to have the upper hand.

Brooklyn had a short bench, as it was without Andray Blatche (bruised left hip), Andrei Kirilenko (sore right calf) and, most notably, Joe Johnson (right knee tendinitis). The veteran guard, who last week earned an All-Star Game nod, Johnson torched the Sixers for a 29-point third quarter that featured eight 3-pointers.

Even without their sharpshooter, the Nets stormed to a 19-4 lead in the game’s opening nine minutes. The Sixers couldn’t shoot (1-for-8) or hold onto the ball (six turnovers) in that span, giving Brooklyn a helping hand.

Whatever it was, the Sixers had it going in the second quarter. From the 3:33 mark of the first, when the Nets were in front by 15, to the 5:30 point of the second, the Sixers outscored the hosts, 38-17, to take a lead. Boos trickled from the upper-deck of the half-full arena.

The reality was that, unlike the first quarter, the Sixers were actually making shots and protecting the basketball.

“Isn’t that amazing how this sport works?” Brown said. “When you actually get to shoot, you have a chance to score. It’s my job. At the end of the day, we talk about it and we haven’t arrested it.

“We play in a crowd. People think we can’t shoot. We go to the line or get to the rim more than anybody in the NBA, so everybody goes under pick-and-rolls and under handoffs, they crowd the paint and we have to learn how to play better in that environment.”

That all changed in the third, when Brooklyn continued a surge that began prior to the break.

With a scoring spree that bridged the second and third quarters, Brooklyn used a 21-5 scoring advantage in a 5-minute, 41-second span. That gave the Nets (21-25) a 63-52, and the game was theirs.

Though it wasn’t without a scare from the Sixers.

NOTES: The revolving door between the NBA and the D-League continues to spin for Lorenzo Brown. The 23-year-old guard got his fifth call-up by the parent club, and was with the Sixers in Brooklyn. … Injured guard Jason Richardson tweeted that he’s been cleared to take jump shots, posting a video of himself doing so at PCOM. It’s his first basketball-related activity since undergoing left-knee surgery last February. … Seattle native Spencer Hawes, who attended Super Bowl XLVIII Sunday in East Rutherford, N.J., said the game “was a ton of fun, from the time you got there.” Hmm, wonder why.